A Class of Two-Sample Distribution-Free Tests for Scale

Abstract

A class of distribution-free statistics for testing equality of two scale parameters when the location parameters are equal is defined. When the two populations are identical, each statistic in this class is governed by the same distribution as that of the two-sample Wilcoxon statistic. A method for selecting which member of the class to use for a particular data set is described, the resulting adaptive procedure being relatively insensitive to small failures in the assumption of equal locations.

Key Words:

• Scale
• Distribution free
• Adaptive